document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200389>Question 1200389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the perimeter and area of the figure pictured below.\r<BR>\n" );
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document.write( "[Graphs generated by this script: initPicture(-6,18,-6,18);path([[0,0],[0,12.5],[3,12.5],[3,2.6],[9.8,2.6],[9.8,0],[0,0]]);text([0,6.25],'12.5 m','left');text([1.5,12.5],'3 m','above');text([9.8,1.3],'2.6 m','right');text([4.9,0],'9.8 m','below');]\r<BR>\n" );
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document.write( "Perimeter = __________________ m<BR>\n" );
document.write( "Area = __________________   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834511 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answers:<BR>\n" );
document.write( "Perimeter = <font color=red>44.6 meters</font><BR>\n" );
document.write( "Area = <font color=red>55.18 square meters</font><BR>\n" );
document.write( "These decimal values are exact without any rounding done to them.\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Starting diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28%0D%0A400%2C400%2C-6%2C18%2C-6%2C18%2C%0D%0Aline%280%2C0%2C+0%2C12.5%29%2C%0D%0Aline%280%2C12.5%2C+3%2C12.5%29%2C%0D%0Aline%283%2C12.5%2C+3%2C2.6%29%2C%0D%0Aline%283%2C2.6%2C+9.8%2C2.6%29%2C%0D%0Aline%289.8%2C2.6%2C+9.8%2C0%29%2C%0D%0Aline%289.8%2C0%2C+0%2C0%29%2C%0D%0Alocate%280-3%2C6.25%2Cmatrix%281%2C2%2C12.5%2C%22m%22%29%29%2C%0D%0Alocate%281.5-0.5%2C12.5%2B1%2Cmatrix%281%2C2%2C3%2C%22m%22%29%29%2C%0D%0Alocate%289.8%2B0.2%2C1.3%2B0.5%2Cmatrix%281%2C2%2C2.6%2C%22m%22%29%29%2C%0D%0Alocate%284.9%2C0%2Cmatrix%281%2C2%2C9.8%2C%22m%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The total vertical height is 12.5 meters<BR>\n" );
document.write( "The far right side small vertical piece is 2.6 meters, meaning the remaining vertical portion is 12.5-2.6 = 9.9 meters\r<BR>\n" );
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document.write( "The total horizontal width is 9.8 meters<BR>\n" );
document.write( "The top side small horizontal piece is 3 meters, meaning the remaining middle horizontal portion is 9.8-3 = 6.8 meters\r<BR>\n" );
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document.write( "Let's update the diagram with those new measurements.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28%0D%0A400%2C400%2C-6%2C18%2C-6%2C18%2C%0D%0Aline%280%2C0%2C+0%2C12.5%29%2C%0D%0Aline%280%2C12.5%2C+3%2C12.5%29%2C%0D%0Aline%283%2C12.5%2C+3%2C2.6%29%2C%0D%0Aline%283%2C2.6%2C+9.8%2C2.6%29%2C%0D%0Aline%289.8%2C2.6%2C+9.8%2C0%29%2C%0D%0Aline%289.8%2C0%2C+0%2C0%29%2C%0D%0Alocate%280-3%2C6.25%2Cmatrix%281%2C2%2C12.5%2C%22m%22%29%29%2C%0D%0Alocate%280%2B3.4%2C6.25%2B2%2Cmatrix%281%2C2%2C9.9%2C%22m%22%29%29%2C%0D%0Alocate%281.5-0.5%2C12.5%2B1%2Cmatrix%281%2C2%2C3%2C%22m%22%29%29%2C%0D%0Alocate%289.8%2B0.2%2C1.3%2B0.5%2Cmatrix%281%2C2%2C2.6%2C%22m%22%29%29%2C%0D%0Alocate%284.9%2C0%2B3.7%2Cmatrix%281%2C2%2C6.8%2C%22m%22%29%29%2C%0D%0Alocate%284.9%2C0%2Cmatrix%281%2C2%2C9.8%2C%22m%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Perimeter = sum of the exterior sides<BR>\n" );
document.write( "Perimeter = 12.5+3+9.9+6.8+2.6+9.8<BR>\n" );
document.write( "Perimeter = <font color=red>44.6 meters</font>\r<BR>\n" );
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document.write( "----------------------------------------------------\r<BR>\n" );
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document.write( "Another approach to find the perimeter:\r<BR>\n" );
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document.write( "Draw vertical and horizontal dashed lines like so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28%0D%0A400%2C400%2C-6%2C18%2C-6%2C18%2C%0D%0Aline%280%2C0%2C+0%2C12.5%29%2C%0D%0Aline%280%2C12.5%2C+3%2C12.5%29%2C%0D%0Aline%283%2C12.5%2C+3%2C2.6%29%2C%0D%0Aline%283%2C2.6%2C+9.8%2C2.6%29%2C%0D%0Aline%289.8%2C2.6%2C+9.8%2C0%29%2C%0D%0Aline%289.8%2C0%2C+0%2C0%29%2C%0D%0Alocate%280-3%2C6.25%2Cmatrix%281%2C2%2C12.5%2C%22m%22%29%29%2C%0D%0Alocate%281.5-0.5%2C12.5%2B1%2Cmatrix%281%2C2%2C3%2C%22m%22%29%29%2C%0D%0Alocate%289.8%2B0.2%2C1.3%2B0.5%2Cmatrix%281%2C2%2C2.6%2C%22m%22%29%29%2C%0D%0Alocate%284.9%2C0%2Cmatrix%281%2C2%2C9.8%2C%22m%22%29%29%2C%0D%0A%0D%0Aline%289.8%2C2.6%2C9.8%2C2.9414%29%2C%0D%0Aline%289.8%2C3.2828%2C9.8%2C3.6241%29%2C%0D%0Aline%289.8%2C3.9655%2C9.8%2C4.3069%29%2C%0D%0Aline%289.8%2C4.6483%2C9.8%2C4.9897%29%2C%0D%0Aline%289.8%2C5.331%2C9.8%2C5.6724%29%2C%0D%0Aline%289.8%2C6.0138%2C9.8%2C6.3552%29%2C%0D%0Aline%289.8%2C6.6966%2C9.8%2C7.0379%29%2C%0D%0Aline%289.8%2C7.3793%2C9.8%2C7.7207%29%2C%0D%0Aline%289.8%2C8.0621%2C9.8%2C8.4034%29%2C%0D%0Aline%289.8%2C8.7448%2C9.8%2C9.0862%29%2C%0D%0Aline%289.8%2C9.4276%2C9.8%2C9.769%29%2C%0D%0Aline%289.8%2C10.1103%2C9.8%2C10.4517%29%2C%0D%0Aline%289.8%2C10.7931%2C9.8%2C11.1345%29%2C%0D%0Aline%289.8%2C11.4759%2C9.8%2C11.8172%29%2C%0D%0Aline%289.8%2C12.1586%2C9.8%2C12.5%29%2C%0D%0A%0D%0A%0D%0Aline%283%2C12.5%2C3.2957%2C12.5%29%2C%0D%0Aline%283.5913%2C12.5%2C3.887%2C12.5%29%2C%0D%0Aline%284.1826%2C12.5%2C4.4783%2C12.5%29%2C%0D%0Aline%284.7739%2C12.5%2C5.0696%2C12.5%29%2C%0D%0Aline%285.3652%2C12.5%2C5.6609%2C12.5%29%2C%0D%0Aline%285.9565%2C12.5%2C6.2522%2C12.5%29%2C%0D%0Aline%286.5478%2C12.5%2C6.8435%2C12.5%29%2C%0D%0Aline%287.1391%2C12.5%2C7.4348%2C12.5%29%2C%0D%0Aline%287.7304%2C12.5%2C8.0261%2C12.5%29%2C%0D%0Aline%288.3217%2C12.5%2C8.6174%2C12.5%29%2C%0D%0Aline%288.913%2C12.5%2C9.2087%2C12.5%29%2C%0D%0Aline%289.5043%2C12.5%2C9.8%2C12.5%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertical dashed line on the far right represents the previous vertical segment that was 9.9 meters tall.<BR>\n" );
document.write( "The horizontal dashed line at the top represents the previous horizontal segment that was 6.8 meters long.\r<BR>\n" );
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document.write( "We have a rectangle after moving those sides or fences around.<BR>\n" );
document.write( "Perimeter of a rectangle = 2*(length + width)<BR>\n" );
document.write( "Perimeter = 2*(9.8+12.5)<BR>\n" );
document.write( "Perimeter = 2*(22.3)<BR>\n" );
document.write( "Perimeter = <font color=red>44.6 meters</font>\r<BR>\n" );
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document.write( "----------------------------------------------------\r<BR>\n" );
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document.write( "Now to find the area\r<BR>\n" );
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document.write( "Let's revisit the original diagram and add in a red vertical line as shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28%0D%0A400%2C400%2C-6%2C18%2C-6%2C18%2C%0D%0Aline%280%2C0%2C+0%2C12.5%29%2C%0D%0Aline%280%2C12.5%2C+3%2C12.5%29%2C%0D%0Aline%283%2C12.5%2C+3%2C2.6%29%2C%0D%0Aline%283%2C2.6%2C+9.8%2C2.6%29%2C%0D%0Aline%289.8%2C2.6%2C+9.8%2C0%29%2C%0D%0Aline%289.8%2C0%2C+0%2C0%29%2C%0D%0Alocate%280-3%2C6.25%2Cmatrix%281%2C2%2C12.5%2C%22m%22%29%29%2C%0D%0Alocate%281.5-0.5%2C12.5%2B1%2Cmatrix%281%2C2%2C3%2C%22m%22%29%29%2C%0D%0Alocate%289.8%2B0.2%2C1.3%2B0.5%2Cmatrix%281%2C2%2C2.6%2C%22m%22%29%29%2C%0D%0Alocate%284.9%2C0%2B3.7%2Cmatrix%281%2C2%2C6.8%2C%22m%22%29%29%2C%0D%0A%0D%0Ared%28line%283%2C0%2C3%2C2.6%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We'll ignore the \"9.8 m\" and go with the 6.8 m instead.\r<BR>\n" );
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document.write( "We have sub-divided the L shape into two rectangles<BR>\n" );
document.write( "left area = 12.5*3 = 37.5<BR>\n" );
document.write( "right area = 6.8*2.6 = 17.68<BR>\n" );
document.write( "total area = left + right = 37.5+17.68 = <font color=red>55.18 square meters</font>\r<BR>\n" );
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document.write( "----------------------------------------------------\r<BR>\n" );
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document.write( "Another way to find the area:\r<BR>\n" );
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document.write( "Revisit the diagram where we added those two dashed segments.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28%0D%0A400%2C400%2C-6%2C18%2C-6%2C18%2C%0D%0Aline%280%2C0%2C+0%2C12.5%29%2C%0D%0Aline%280%2C12.5%2C+3%2C12.5%29%2C%0D%0Aline%283%2C12.5%2C+3%2C2.6%29%2C%0D%0Aline%283%2C2.6%2C+9.8%2C2.6%29%2C%0D%0Aline%289.8%2C2.6%2C+9.8%2C0%29%2C%0D%0Aline%289.8%2C0%2C+0%2C0%29%2C%0D%0Alocate%280-3%2C6.25%2Cmatrix%281%2C2%2C12.5%2C%22m%22%29%29%2C%0D%0Alocate%280%2B3.4%2C6.25%2B2%2Cmatrix%281%2C2%2C9.9%2C%22m%22%29%29%2C%0D%0Alocate%281.5-0.5%2C12.5%2B1%2Cmatrix%281%2C2%2C3%2C%22m%22%29%29%2C%0D%0Alocate%289.8%2B0.2%2C1.3%2B0.5%2Cmatrix%281%2C2%2C2.6%2C%22m%22%29%29%2C%0D%0Alocate%284.9%2C0%2B3.7%2Cmatrix%281%2C2%2C6.8%2C%22m%22%29%29%2C%0D%0Alocate%284.9%2C0%2Cmatrix%281%2C2%2C9.8%2C%22m%22%29%29%2C%0D%0A%0D%0Aline%289.8%2C2.6%2C9.8%2C2.9414%29%2C%0D%0Aline%289.8%2C3.2828%2C9.8%2C3.6241%29%2C%0D%0Aline%289.8%2C3.9655%2C9.8%2C4.3069%29%2C%0D%0Aline%289.8%2C4.6483%2C9.8%2C4.9897%29%2C%0D%0Aline%289.8%2C5.331%2C9.8%2C5.6724%29%2C%0D%0Aline%289.8%2C6.0138%2C9.8%2C6.3552%29%2C%0D%0Aline%289.8%2C6.6966%2C9.8%2C7.0379%29%2C%0D%0Aline%289.8%2C7.3793%2C9.8%2C7.7207%29%2C%0D%0Aline%289.8%2C8.0621%2C9.8%2C8.4034%29%2C%0D%0Aline%289.8%2C8.7448%2C9.8%2C9.0862%29%2C%0D%0Aline%289.8%2C9.4276%2C9.8%2C9.769%29%2C%0D%0Aline%289.8%2C10.1103%2C9.8%2C10.4517%29%2C%0D%0Aline%289.8%2C10.7931%2C9.8%2C11.1345%29%2C%0D%0Aline%289.8%2C11.4759%2C9.8%2C11.8172%29%2C%0D%0Aline%289.8%2C12.1586%2C9.8%2C12.5%29%2C%0D%0A%0D%0A%0D%0Aline%283%2C12.5%2C3.2957%2C12.5%29%2C%0D%0Aline%283.5913%2C12.5%2C3.887%2C12.5%29%2C%0D%0Aline%284.1826%2C12.5%2C4.4783%2C12.5%29%2C%0D%0Aline%284.7739%2C12.5%2C5.0696%2C12.5%29%2C%0D%0Aline%285.3652%2C12.5%2C5.6609%2C12.5%29%2C%0D%0Aline%285.9565%2C12.5%2C6.2522%2C12.5%29%2C%0D%0Aline%286.5478%2C12.5%2C6.8435%2C12.5%29%2C%0D%0Aline%287.1391%2C12.5%2C7.4348%2C12.5%29%2C%0D%0Aline%287.7304%2C12.5%2C8.0261%2C12.5%29%2C%0D%0Aline%288.3217%2C12.5%2C8.6174%2C12.5%29%2C%0D%0Aline%288.913%2C12.5%2C9.2087%2C12.5%29%2C%0D%0Aline%289.5043%2C12.5%2C9.8%2C12.5%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let<BR>\n" );
document.write( "A = area of the larger rectangle<BR>\n" );
document.write( "B = area of the smaller rectangle<BR>\n" );
document.write( "The idea is to find each area and then subtract those results.\r<BR>\n" );
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document.write( "A = 12.5*9.8 = 122.5<BR>\n" );
document.write( "B = 9.9*6.8 = 67.32<BR>\n" );
document.write( "A-B = 122.5 - 67.32 = <font color=red>55.18 square meters</font><BR>\n" );
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